Motivated by ecological communities to develop tools for multi-dimensional time series
Collage of rodent species from the Portal Project; https://portal.naturecast.org/profiles.html
Background
Background
Motivated by ecological communities to develop tools for multi-dimensional time series
Time series of rodent populations
Background
Motivated by ecological communities to develop tools for multi-dimensional time series
Time series of rodent populations with putative qualitative changes noted
Background
Quantify how ecosystems are responding to stressors
- Climate change
- Invasive species
- Landscape alteration
Phase plane of precipitation and temperature at Portal over time
Background
- Stochasticity
- Autocorrelation
- Cyclical dynamics
- Gradual change
- Abrupt shifts
Time series of rodent populations zoomed in to moons 200 to 400
Background
Title of Christensen et al 2018 Ecology Report
Christensen et al. 2018 established methods
Background
LDATS: Latent Dirichlet Allocation coupled with Time Series analyses
Christensen et al. 2018 established methods
Background (coming soon!)
LDATS: Linguistic Decomposition Algorithms coupled with Time Series analyses
Christensen et al. 2018 established methods
Goals for LDATS Package
- Standardize, Generalize, Optimize Christensen et al. 2018 methodology
lm-style analysis API
Digital painting of horses coming out from under the hood of a truck; https://www.deviantart.com/sesroh/art/235-Horses-Under-The-Hood-52286525
Goals for LDATS Package
LDA_TS(data, topics = 2, replicates = 1, formulas = ~1, nchangepoints = 0, timename = "time", weights = TRUE, control = list())
Screencap of LDATS on CRAN; https://cran.r-project.org/web/packages/LDATS/index.html
Statistical Approach
Two-stage analyses:
- Reduce dimensions
- Analyze time series from [1]
Dimension Reduction
Latent Dirichlet Allocation
\(M\) total documents
\(N\) total words
\(w\) term identity
\(z\) topic identity
\(\theta\) topics-in-documents
\(\alpha\) Dirichlet parameter for \(\theta\)
\(\beta\) terms-in-topics
Plate notation for Latent Dirichlet Allocation
Bookshelf
Dimension Reduction
Latent Dirichlet Allocation
Matrix decomposition representation of LDA
Bookshelf
Dimension Reduction
Latent Dirichlet Allocation
Matrix decomposition representation of LDA with ecological terms
Collage of rodent species from the Portal Project; https://portal.naturecast.org/profiles.html
Dimension Reduction
Latent Dirichlet Allocation
Matrix decomposition representation of LDA with ecological terms and Gamma bolded
Collage of rodent species from the Portal Project; https://portal.naturecast.org/profiles.html
Time Series
Multivariate response with a suite of possible dynamics
Time series of LDA decomposed rodent data
Time Series
Multivariate response
Softmax-based regression via nnet
\[S(y_i) = \frac{e^y_i}{\sum_je^y_j}\]
Time Series (coming soon!)
Multivariate response
Simplex-based regression via compositions
\[\mathrm{ILR}(y_i) = \sqrt{\frac{i}{i+1}}\mathrm{ln}(\frac{\overline{\mathbf{x}}}{x_{i+1}}) \]
Time Series
Bayesian Change Point Indicator Regression
Change Point time series from Ruggieri paper showing application of multi-change point model to NOAA temperature anomaly data
Time Series
Bayesian Change Point Indicator Regression
- 0, 1, … change points
- varying dynamics between change points
Time series of LDA decomposed rodent data
Time Series
Sequential fitting:
- Posterior probability of change points, unconditional on regressors
- produces estimates of regressors conditional on change points
- De-condition posterior probabilities of regressors given uncertain change points
Time Series
Time series of LDA decomposed rodent data analyzed using the time series model, with change points and fitted dynamics shown
Time Series
Estimation via parallel tempering Markov Chain Monte Carlo (ptMCMC) over the top of multinomial regression
Figure 1 from Earl and Deem 2005 showing a 2-D representation of a phase space for which ptMCMC is useful
Figure 2 from Earl and Deem 2005, a schematic of parallel tempering chains with swapping
Time Series
Estimation via parallel tempering Markov Chain Monte Carlo (ptMCMC) over the top of multinomial regression
Coded internally in LDATS functions
Digital painting of horses coming out from under the hood of a truck; https://www.deviantart.com/sesroh/art/235-Horses-Under-The-Hood-52286525
LDATS Package
Top-level API:
LDA_TS(data, topics = 2, nseeds = 1, formulas = ~1, nchangepoints = 0, timename = "time", weights = TRUE, control = list())
Multi-model friendly
Down-and-dirty details in control lists
LDATS Package (coming soon!)
Top-level API v0.3.0:
LDA_TS(data, topics = 2, replicates = 1, formulas = ~1, nchangepoints = 0, timename = "time", weights = TRUE, control = list())
Multi-model friendly
Down-and-dirty details in control lists
LDATS Package
Vignettes
- show full application
- compare package to Christensen et al. 2018
- detail codebase
LDATS Package
Internally-conducted summaries
ldats <- LDA_TS(data)
ldats[["Selected TS model"]][["rho_summary"]]
| Mean | Median | Mode | Lower95 | Upper95 | SD | MCMCerr | AC10 | ESS |
|---|---|---|---|---|---|---|---|---|
| 209.3 | 211 | 215 | 190 | 225 | 9.7 | 0.307 | 0.01 | 380.35 |
LDATS Package
Internally-conducted summaries
ldats <- LDA_TS(data)
ldats[["Selected TS model"]][["eta_summary"]]
LDATS Package
| Mean | Median | Lower_95. | Upper_95. | SD | MCMCerr | AC10 | ESS | |
|---|---|---|---|---|---|---|---|---|
| 1_2:(Intercept) | 4.0036 | 4.0243 | 1.6620 | 6.8060 | 1.3454 | 0.0425 | 0.0094 | 1000.0000 |
| 1_2:sin_year | -0.3418 | -0.4003 | -3.6011 | 3.0493 | 1.7426 | 0.0551 | 0.0262 | 1000.0000 |
| 1_2:cos_year | -0.0026 | -0.0498 | -3.7253 | 3.2932 | 1.8382 | 0.0581 | 0.0163 | 1000.0000 |
| 1_3:(Intercept) | 4.6038 | 4.5977 | 1.9996 | 7.2317 | 1.3397 | 0.0424 | 0.0038 | 1000.0000 |
| 1_3:sin_year | -0.0342 | -0.1448 | -3.2549 | 3.3501 | 1.7418 | 0.0551 | 0.0349 | 1000.0000 |
| 1_3:cos_year | 0.0358 | -0.0341 | -3.5637 | 3.4618 | 1.8196 | 0.0575 | 0.0276 | 1000.0000 |
| 1_4:(Intercept) | 4.1062 | 4.1398 | 1.6778 | 6.8296 | 1.3486 | 0.0426 | 0.0040 | 1000.0000 |
| 1_4:sin_year | 0.3525 | 0.2968 | -3.2788 | 3.3958 | 1.7471 | 0.0552 | 0.0432 | 1000.0000 |
| 1_4:cos_year | 0.8800 | 0.8270 | -2.4651 | 4.4997 | 1.8530 | 0.0586 | 0.0208 | 1000.0000 |
| 1_5:(Intercept) | 1.6518 | 1.7057 | -1.5298 | 4.3376 | 1.5107 | 0.0478 | 0.0073 | 1000.0000 |
| 1_5:sin_year | -0.5321 | -0.5591 | -3.9735 | 3.2118 | 1.8668 | 0.0590 | 0.0224 | 1000.0000 |
| 1_5:cos_year | -0.8481 | -0.8340 | -4.5197 | 2.9822 | 1.9928 | 0.0630 | 0.0329 | 1000.0000 |
| 2_2:(Intercept) | -0.0674 | -0.0660 | -0.3786 | 0.2384 | 0.1585 | 0.0050 | 0.0253 | 1000.0000 |
| 2_2:sin_year | 0.2567 | 0.2568 | -0.1634 | 0.6372 | 0.2051 | 0.0065 | -0.0278 | 1000.0000 |
| 2_2:cos_year | 0.2549 | 0.2577 | -0.1682 | 0.6894 | 0.2195 | 0.0069 | -0.0247 | 1000.0000 |
| 2_3:(Intercept) | -3.1093 | -3.0894 | -4.1536 | -2.1059 | 0.5211 | 0.0165 | -0.0045 | 1000.0000 |
| 2_3:sin_year | -0.2543 | -0.2546 | -1.4403 | 1.0769 | 0.6797 | 0.0215 | -0.0112 | 1000.0000 |
| 2_3:cos_year | 0.0130 | -0.0209 | -1.4893 | 1.4148 | 0.7356 | 0.0233 | 0.0099 | 1000.0000 |
| 2_4:(Intercept) | -1.5830 | -1.5814 | -2.1843 | -1.0077 | 0.2980 | 0.0094 | 0.0283 | 1000.0000 |
| 2_4:sin_year | 0.8906 | 0.8970 | 0.1771 | 1.5999 | 0.3670 | 0.0116 | 0.0108 | 661.4502 |
| 2_4:cos_year | 1.0036 | 0.9791 | 0.2897 | 1.7794 | 0.3838 | 0.0121 | -0.0294 | 1000.0000 |
| 2_5:(Intercept) | -0.0806 | -0.0848 | -0.3907 | 0.2675 | 0.1702 | 0.0054 | 0.0110 | 1000.0000 |
| 2_5:sin_year | -0.2238 | -0.2135 | -0.6292 | 0.1596 | 0.2078 | 0.0066 | 0.0292 | 1000.0000 |
| 2_5:cos_year | -0.8205 | -0.8260 | -1.2504 | -0.3399 | 0.2363 | 0.0075 | 0.0011 | 1000.0000 |
LDATS Package
Plotting functionality
ldats <- LDA_TS(data)
plot(ldats)
LDATS Package
Time series of LDA decomposed rodent data
Time series of LDA decomposed rodent data analyzed using the time series model, with change points and fitted dynamics shown
LDATS Package
LDATS Package
simulatepredictflexible model selection methods
- hold out & cross-validation
Application
Context: Macro-ecological Analyses of Time Series Structure (MATSS)
Leverage a massive compendium of ecological time series to evaluate the presence of, e.g., regime shifts
Application
Results of LDATS analyses for many ecological communities
Interested?
We welcome collaborators and contributors!
Acknowledgements
Funding
National Science Foundation: DEB-1622425, DGE-1315138, DGE-1842473
Gordon and Betty Moore Foundation: Data-Driven Discovery Initiative Grant GBMF4563
Weecology, DAPPER Stats, and UF logos